Thanks for your answer! I not sure if I understand the remote desktop thing though. Today's date on my computer is 2016-08-11
In one sheet it looks like this:
In another sheet it looks like this:
Note that Im using different datasources and different dimensions: but it's still a mystery to me. Should Tableau just take the (todays date) from my computer?
Tableau takes "today" from the data source, not from your computer.
In the screenshots that you posted, the databases are set to different time zones. It's not uncommon for servers to use UTC (Universal Time Coordinated) rather than local time. You may have to use calculated times with dateadd() to correct, or build views on the database that correct to local time.